Yes, even though the PIC is the ultimate authority in the operation of the aircraft, the handling of this emergency by the pilot is definitely NOT professional, IMHO. The pilot declared an emergency, which he has a right to do if there truly was an emergency. Per the FAA and review of the FAR's and AIM, the pilot should then wait for an amendend clearance from ATC unless the emergency requires immediate and continued deviation from the FAR's. It doesn't sound like it was a control issue (entered a turn to do a circle to land at another runway), engine issue (as it doesn't sound like any issues in doing a circle to land which would have required multiple power adjustments), etc. The controller acknowledged the emergency and altered the clearance, instructing the pilot to fly runway heading so that he could most likely get the pilot down with minimal disruption to other airport operations. Instead, he turned on his own, causing ATC to scramble to get other planes out of the way, sending other pilots scrambling to do go-arounds and new approaches, etc. In my opinion, as a pilot myself, the pilot of AA0002 in this case was out of line. If the emergency was a true emergency, I'm SURE this would be all over the news by now.
When an emergency is declared in the terminal area, the tower is supposed to log the details, tapes, etc. and report it to the FSDO. This doesn't always happen, but I can guarantee this incident will definitely be reported by the tower to the FSDO based solely on the tone and animosity that was developing between the controller and the pilot. I wonder if we'll ever get the details.